Which linear equation has the same solution set as 9d4+3−2d=−2(3+d) ?(1 point) Responses
4w−2(7−3w)=w/3−6
14=7/4x−19/4+2x
35−15b=95
3x/5−10=−7
To find the linear equation that has the same solution set as 9d4+3−2d=−2(3+d), we can start by simplifying the given equation.
9d4 + 3 - 2d = -2(3 + d)
Expanding the right side of the equation:
9d4 + 3 - 2d = -6 - 2d
Next, we can combine like terms on both sides of the equation:
9d4 + 3 - 2d + 2d = -6 - 2d + 2d
9d4 + 3 = -6
Now, we can solve for d:
9d4 = -9
d4 = -1
Taking the fourth root of both sides:
d = -1
So, the linear equation that has the same solution set as 9d4+3−2d=−2(3+d) is:
d = -1
Therefore, the correct answer is "3x/5−10=−7".
To find the linear equation that has the same solution set as the given equation, we need to simplify the given equation and rearrange it in the standard form (ax + b = c) of a linear equation.
Let's start by simplifying the given equation:
9d4 + 3 - 2d = -2(3 + d)
Multiply -2 with each term inside the parentheses:
9d4 + 3 - 2d = -6 - 2d
Now, let's add 2d to both sides to get all the d terms on one side of the equation:
9d4 + 3 = -6
Next, subtract 3 from both sides:
9d4 = -6 - 3
9d4 = -9
Finally, divide both sides by 9 to isolate d:
d4 = -1
The equation d4 = -1 does not represent a linear equation, as it has a power of 4. Therefore, none of the provided options can have the same solution set.
To find the linear equation that has the same solution set as 9d4+3−2d=−2(3+d), we need to isolate the variable "d" on one side of the equation.
Let's simplify the equation step-by-step:
1. Distribute the "-2" on the right side:
9d + 4 + 3 - 2d = -2(3 + d)
9d + 4 + 3 - 2d = -6 - 2d
2. Combine like terms on both sides of the equation:
9d - 2d + 7 = -6 - 2d
3. Add 2d to both sides to isolate the "d" terms on one side:
9d - 2d + 2d + 7 = -6 - 2d + 2d
9d + 7 = -6
4. Subtract 7 from both sides to further isolate the "d" terms:
9d + 7 - 7 = -6 - 7
9d = -13
5. Divide both sides by 9 to solve for "d":
(9d) / 9 = (-13) / 9
d = -13/9
Now that we have the solution for "d" as -13/9, let's check the answer choices to find the linear equation with the same solution:
A) 4w - 2(7 - 3w) = w/3 - 6
B) 14 = 7/4x - 19/4 + 2x
C) 35 - 15b = 95
D) 3x/5 - 10 = -7
Substituting d = -13/9 into each equation:
A) 4w - 2(7 - 3w) = w/3 - 6
This equation does not involve the variable "d", so it does not have the same solution set.
B) 14 = 7/4x - 19/4 + 2x
This equation also does not involve the variable "d", so it does not have the same solution set.
C) 35 - 15b = 95
This equation does not involve the variable "d" either, so it does not have the same solution set.
D) 3x/5 - 10 = -7
This equation also does not involve the variable "d", so it does not have the same solution set.
None of the given answer choices have the same solution set as the original equation 9d + 4 + 3 - 2d = -2(3 + d).